2014 April(71H) Math Question 1
Choice A
it says that "Danica will donate $35.00, plus $0.07 for each book donated by her classmates.", and that her classmates donated b books:
d = 35 + 0.07b
2014 April(71H) Math Question 2
Choice K
z = -16 × (-4) = 64
2014 April(71H) Math Question 3
Choice D
Rule name |
Rule |
Example |
Product rules |
a^{ n} ⋅ a^{ m} = a^{ n+m} |
2^{3} ⋅ 2^{4} = 2^{3+4} = 128 |
a^{ n} ⋅ b^{ n} = (a ⋅ b)^{ n} |
3^{2} ⋅ 4^{2} = (3⋅4)^{2} = 144 |
Quotient rules |
a^{ n} / a^{ m} = a^{ n}^{–m} |
2^{5} / 2^{3} = 2^{5-3} = 4 |
a^{ n} / b^{ n} = (a / b)^{ n} |
4^{3} / 2^{3} = (4/2)^{3} = 8 |
Power rules |
(b^{n})^{m} = b^{n⋅m} |
(2^{3})^{2} = 2^{3⋅2} = 64 |
_{b}n^{m} _{= b}(n^{m}) |
_{2}3^{2} _{= 2}(3^{2})_{= 512} |
^{m}√(b^{n}) = b ^{n/m} |
^{2}√(2^{6}) = 2^{6/2} = 8 |
b^{1/n} = ^{n}√b |
8^{1/3} = ^{3}√8 = 2 |
Negative exponents |
b^{-n} = 1 / b^{n} |
2^{-3} = 1/2^{3} = 0.125 |
Zero rules |
b^{0} = 1 |
5^{0} = 1 |
0^{n} = 0 , for n>0 |
0^{5} = 0 |
One rules |
b^{1} = b |
5^{1} = 5 |
1^{n} = 1 |
1^{5} = 1 |
Minus one rule |
(-1)^{n} = -1 , n odd v
(-1)^{n} = 1 , n even |
(-1)^{5} = -1 |
Derivative rule |
(x^{n})‘ = n⋅x^{ n}^{-1} |
(x^{3})‘ = 3⋅x^{3-1} |
Integral rule |
∫ x^{n}dx = x^{n}^{+1}/(n+1)+C |
∫ x^{2}dx = x^{2+1}/(2+1)+C |
4b8⋅5b3 = 4⋅5⋅b8+3=20b11
2014 April(71H) Math Question 4
Choice K
The Exterior Angle Theorem states that, for a triangle:
- The exterior angle d equals the angles a plus b
- The exterior angle d is greater than angle a, or angle b.
Therefore, ∠PRS = 40° + 105° = 145°
2014 April(71H) Math Question 5
Choice D
Let the larger number be L, the smaller number be S:
L + S = 90
L = S + 50
⇒ S = 20, L = 70
2014 April(71H) Math Question 6
Choice G
The absolute value of a number is its distance from zero on a number line.
|7 - 5| - |1 - 8| = 2 - 7 = -5
2014 April(71H) Math Question 7
Choice E
$$3^{2}+2+(-3)^{2}-3=17$$
2014 April(71H) Math Question 8
Choice G
$$(x^{2}+2x)+(3x+5)+(x^{2}+1)+(6x-4)$$
$$=(x^{2}+x^{2})+(2x+3x+6x)+(5+1-4)$$
$$=2x^{2}+11x+2$$
2014 April(71H) Math Question 9
Choice E
Let the number of Tough Cuts be T, the number of Easy Pushes be E,
T + E = 96
T = 2E
⇒ E = 32, T = 64
2014 April(71H) Math Question 10
Choice H
The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) -- or, if there are an even number of data, the median is the average of the middle two numbers.
In descending order, the set of numbers is:
116, 142, 175, 186, 191, 201, 201
Median = 186
2014 April(71H) Math Question 11
Choice C
(50 – 20) inches / 5 years = 6 inches
2014 April(71H) Math Question 12
Choice G
The area of a triangle is given by the equation:
Area_{△ }= (1/2) × base × height
Therefore,
Area_{△ }= (1/2) × 16 × 12 = 96
2014 April(71H) Math Question 13
Choice C
($3.36 – $0.16) ÷ 4 × 6= $4.8
2014 April(71H) Math Question 14
Choice H
Midpoint of a Line Segment
The midpoint is halfway between the two end points:
- Its x value is halfway between the two x values
- Its y value is halfway between the two y values
To calculate it:
- Add both “x” coordinates, divide by 2
- Add both “y” coordinates, divide by 2
x = (1/2) × (0 + 300) = 150
y = (1/2) × (0 + 160) = 80
2014 April(71H) Math Question 15
Choice C
Distance between two points P(x1, y1) and Q(x2, y2) is given by:
$$d(P,Q) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$$
Distance of a point P(x, y) from the origin is given by:
$$d(0,P) = \sqrt{x^2+y^2}$$
Therefore,
$$d(0,Bright\ City) = \sqrt{300^2+160^2}= 340$$
which is between 300 and 390.
2014 April(71H) Math Question 16
Choice J
390 ÷ 32 × $2.25 = $27.42 ≈ $27
2014 April(71H) Math Question 17
Choice A
For any fraction, the greater its numerator and the lessor its denominator, the greater the value of the fraction.
Among the choices, d / a has the greatest numerator d and the least denominator a.
2014 April(71H) Math Question 18
Choice J
Let the number of extra hours Maurice worked beyond 40 hours be E:
$12.5 × 40 + $18.75 × E = $931.25
⇒ E = 23
⇒ Total hours = 40 + 23 = 63 hours
2014 April(71H) Math Question 19
Choice B
8 × 10 + 12 × 14 + 10 × 12 + 12 × 12 =
2014 April(71H) Math Question 20
Choice H
The perimeter of a parallelogram can be found by the formula:
perimeter = 2(w+h)
where:
w is the base length of the parallelogram
h is the side length
80 = 2 (18 + h)
⇒ h = 22
The other sides are: 18, 22, 22.
2014 April(71H) Math Question 21
Choice A
Thus, tan N = 6/11
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2014 April(71H) Math Question 22
Choice J
The volume of a right …
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2014 April(71H) Math Question 23
Choice A
The perimeter of a rectangle …
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2014 April(71H) Math Question 24
Choice F
The cube has 2 stars …
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2014 April(71H) Math Question 25
Choice C
First off, we need to …
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2014 April(71H) Math Question 26
Choice F
Plugging the numbers into the …
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2014 April(71H) Math Question 26
Choice F
Plugging the numbers into the …
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2014 April(71H) Math Question 27
Choice B
Two triangles are said to …
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2014 April(71H) Math Question 28
Choice K
The measure of a straight …
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2014 April(71H) Math Question 29
Choice A
Given any two points on …
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2014 April(71H) Math Question 30
Choice K
(2x – 3)(-x – 7) = (2x …
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2014 April(71H) Math Question 31
Choice C
The perimeter of a circle …
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2014 April(71H) Math Question 32
Choice F
Since there are a total …
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2014 April(71H) Math Question 33
Choice E
The expression ” the product of …
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2014 April(71H) Math Question 34
Choice J
The quadratic formula for the …
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2014 April(71H) Math Question 35
Choice C
Generally, The area of a …
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2014 April(71H) Math Question 36
Choice F
It says that “rental fee …
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2014 April(71H) Math Question 37
Choice A
Any line parallel to the …
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2014 April(71H) Math Question 38
Choice G
Let’s refresh the definitions …
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2014 April(71H) Math Question 39
Choice C
Such integers can be:
1 …
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2014 April(71H) Math Question 40
Choice G
By definition, each side of …
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2014 April(71H) Math Question 41
Choice D
Simplifying the equation, we have …
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2014 April(71H) Math Question 42
Choice F
$1.5 / 125 = $0.012 …
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2014 April(71H) Math Question 43
Choice C
Let’s divide all the …
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2014 April(71H) Math Question 44
Choice F
Let the number of Style …
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2014 April(71H) Math Question 45
Choice D
200 × 1.6 = 320
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2014 April(71H) Math Question 46
Choice J
3x + 5y = 17 (i)
2x …
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2014 April(71H) Math Question 47
Choice E
The least common multiple is …
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2014 April(71H) Math Question 48
Choice G
The slopes of two lines …
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2014 April(71H) Math Question 49
Choice A
Graphing an inequality on a …
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2014 April(71H) Math Question 50
Choice G
Total surface area = ½ × 3 …
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2014 April(71H) Math Question 51
Choice C
1 # 2 = 1 + 2 = 3 …
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2014 April(71H) Math Question 52
Choice G
When a point is translated …
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2014 April(71H) Math Question 53
Choice C
What you need to know …
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2014 April(71H) Math Question 54
Choice K
What is looks like is …
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2014 April(71H) Math Question 55
Choice D
When parallel lines get crossed …
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2014 April(71H) Math Question 56
Choice G
ME = AM – AE = AM – BN …
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2014 April(71H) Math Question 57
Choice E
It should be remembered that …
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2014 April(71H) Math Question 58
Choice F
We should recognize that the …
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2014 April(71H) Math Question 59
Choice D
An arithmetic sequence is a …
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2014 April(71H) Math Question 60
Choice K
The graph crosses the x-axis …
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